The ESO Slice Project (ESP) galaxy redshift survey. VII. The redshift and real-space correlation functions

We present analyses of the two-point correlation properties of the ESO Slice Project (ESP) galaxy redshift survey, both in redshift and real space. From the redshift-space correlation function $xi (r) i(s) we are able to trace positive clustering out to separations as large as 50 h^{-1} Mpc, after which xi (r) i(s) smoothly breaks down, crossing the zero value between 60 and 80 h^{-1} Mpc. This is best seen from the whole magnitude-limited redshift catalogue, using the J_3 miniμm-variance weighting estimator. xi (r) i(s) is reasonably well described by a shallow power law with \gamma\sim 1.5 between 3 and 50 h^{-1} Mpc, while on smaller scales (0.2-2 h^{-1} Mpc) it has a shallower slope (\gamma\sim 1). This flattening is shown to be mostly due to the redshift-space damping produced by virialized structures, and is less evident when volume-limited samples of the survey are analysed. We examine the full effect of redshift-space distortions by computing the two-dimensional correlation function xi (r) i(r_p,\pi) , from which we project out the real-space xi (r) i(r) below 10 h^{-1} Mpc. This function is well described by a power-law model (r/r_o)^{-\gamma}, with r_o=4.15^{+0.20}_{-0.21} h^{-1} Mpc and \gamma=1.67^{+0.07}_{-0.09} for the whole magnitude-limited catalogue. Comparison to other redshift surveys shows a consistent picture in which galaxy clustering remains positive out to separations of 50 h^{-1} Mpc or larger, in substantial agreement with the results obtained from angular surveys like the APM and EDSGC. Also the shape of the two-point correlation function is remarkably unanimous among these data sets, in all cases requiring more power on scales larger than 5 h^{-1} Mpc (a `shoulder'), with respect to a simple extrapolation of the canonical xi (r) i(r) =(r/5)^{-1.8}. The analysis of xi (r) i(s) for volume-limited subsamples with different luminosity shows evidence of luminosity segregation only for the most luminous sample with M_{b_J} <= -20.5. For these galaxies, the amplitude of clustering is on all scales >4 h^{-1} Mpc about a factor of 2 above that of all other subsamples containing less luminous galaxies. When redshift-space distortions are removed through projection of xi (r) i(r_p,\pi) , however, a weak dependence on luminosity is seen at small separations also at fainter magnitudes, resulting in a growth of r_o from 3.45_{-0.30}^{+0.21} h^{-1} Mpc to 5.15_{-0.44}^{+0.39} h^{-1} Mpc, when the limiting absolute magnitude of the sample changes from M=-18.5 to M=-20. This effect is masked in redshift space, as the mean pairwise velocity dispersion experiences a parallel increase, basically erasing the effect of the clustering growth on xi (r) i(s) . Based on observations collected at the European Southern Observatory, La Silla, Chile.}